Index Laws
- Qs
- 6
- Marks
- 6
NameDateScore / 6
1.[1]
Work out 22.
2.[1]
Work out 32.
3.[1]
Work out 22.
4.[1]
Work out 22.
5.[1]
Work out 22.
6.[1]
Work out 53.
Answer key
- 42 × 2 = 4
- 93 × 3 = 9
- 42 × 2 = 4
- 42 × 2 = 4
- 42 × 2 = 4
- 1255 × 5 × 5 = 125
Index Laws: Year 8 maths
Students apply laws of indices to simplify expressions involving powers with common bases. The exercises cover multiplication, division, powers of powers, and negative or fractional exponents.
What this covers
Index Laws is taught in Year 8 (age 13 to 14) as a main teaching focus. It sits in the Number strand.
Worked example
Simplify (x^5 × x^3) ÷ x^2.
- Apply the product rule to the numerator: x^(5+3) = x^8
- Apply the quotient rule: x^(8-2) = x^6
- The simplified result is x^6
Answer: x^6
Difficulty scale
The sheet generator offers five difficulty settings for this topic.
- Product and quotient laws with positive integer indices on a single variable
- Power of a power rule and zero index (e.g. (a^3)^2, b^0)
- Expressions with coefficients and multiple variables (e.g. 3a^2 × 4a^3)
- Negative integer indices (e.g. x^-2 = 1/x^2) and numerical evaluations
- Fractional indices and combinations of roots and powers (e.g. 27^(23))
Common mistakes
- Multiplying the powers instead of adding them when multiplying bases (e.g. x^2 * x^3 = x^6)
- Applying the power to the coefficient without brackets (e.g. treating 2x^3 as (2x)^3)
Curriculum links
Indicative matches to Australian Curriculum v9. Check wording and codes against the official document.
- AC9M8N01 Apply index laws with positive integer powers to simplify numerical and algebraic expressions.
Sample sheet and answers
Six questions at the level's usual difficulty. Open the editor to change, add or regenerate any of them.